Synthesis and characterization of iPP‐sPP stereoblock produced by a binary metallocene system

Stereoblock polypropylenes comprising of iPP and sPP segments are synthesized by polymerization of the following binary system of metallocenes: the C_s‐symmetric [2,7‐t‐Bu₂(Flu)₂Ph₂C(Cp)ZrCl₂] and the C₂‐symmetric rac‐Me₂Si(2‐Me‐4‐Ph‐Ind)₂ZrCl₂. Blends of samples made either by each catalyst individually (solution blend) with materials obtained with the mixed catalyst system (reactor blend) are compared. The simultaneous presence of MAO and DEZ, enhancing fast and reversible transfer of the growing chains between the two active centers, leads to the formation of a stereoblock microstructure. In this case, low molecular weight polymers are obtained. The junction between the blocks is qualitatively observed in ¹³C NMR. When made in toluene, the stereoblock material consists of a majority of syndiotactic sequences, whereas the ratio is more equilibrated when the polymerization was conducted in the more polar chlorobenzene. This is confirmed by the results obtained with ¹³C NMR, CRYSTAF, HT HPLC, DSC, SSA, WAXD, and optical microscopy. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1422–1434     

Growth Rates and Explosions in Sandpiles

We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in ? ^d . Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h≤2d?2, the diameter of the set of sites that topple has order n ^1/d . This was previously known only for h<d. Our proof uses a strong form of the least action principle for sandpiles, and a novel method of background modification. We can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d?1. On the other hand, we show that if the background height 2d?2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random, then adding finitely many particles creates an explosion (a sandpile that never stabilizes).